Question 821708: Redwood Growth
The growth, f(x), in inches per year of a redwood tree less than 30 years old is given by the function f(x)= -0.02x^2+x+1, where x represents the number of inches of rainfall per year.
a)Find the growth per year of a redwood tree in a year in which there is 12 inches of rainfall.
b) If the growth of a redwood tree in one year is 10 inches, find the number of inches of rainfall for that year. Round answer to 2 decimal places.
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
f(x) = -0.02x^2 + x + 1
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answer a:
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when rainfall is 12 inches per year (x = 12):
f(12) = -0.02(12)^2 + 12 + 1
f(12) = 10.12 inches growth per year when x=12 inches of rainfall that year
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answer b:
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when tree growth is 10 inches per year (f(x) = 10):
f(x) = 10 = -0.02x^2 + x + 1
-0.02x^2 + x - 9 = 0
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the above quadratic equation is in standard form, with a=-0.02, b=1, and c=-9
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
-0.02 1 -9
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the two real roots (i.e. the two x-intercepts), of the quadratic are:
x = 11.7712434
x = 38.2287566
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10 inches of growth per year occurs under two distinct conditions:
condition 1: rainfall = 11.8 inches for that year
condition 2: rainfall = 38.2 inches for that year
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Solve quadratic equations, quadratic formula:
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Solve systems of linear equations up to 6-equations 6-variables:
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